In a data storage system, a cache is managed by a predictive cache management engine that evaluates cache contents and purges entries unlikely to receive sufficient future cache hits. The engine includes a single output back propagation neural network that is trained in response to various event triggers. Accesses to stored datasets are logged in a data access log; conversely, log entries are removed according to a predefined expiration criteria. In response to access of a cached dataset or expiration of its log entry, the cache management engine prepares training data. This is achieved by determining characteristics of the dataset at various past times between the time of the access/expiration and a time of last access, and providing these characteristics and the times of access as input to train the neural network. As another part of training, the cache management engine provides the neural network with output representing the expiration or access of the dataset. According to a predefined schedule, the cache management engine operates the trained neural network to generate scores for cached datasets, these scores ranking the datasets relative to each other. According to this or a different schedule, the cache management engine reviews the scores, identifies one or more datasets with the least scores, and purges the identified datasets from the cache.